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August 10, 2011

Significant figures are significant

Have you heard about the Global Physics Department Meetings? Physics teachers (high school and college) meet online every Wednesday night for about an hour to chat about a topic related to teaching physics.

This week the topic is about uncertainty, error propagation and significant figures. It seems that there is no shortage of physics teachers who are opposed to teaching about and requiring students to use significant figures.

Count me in the camp which thinks significant figures have a place in our classes and labs that we run.

Here's why:

The goal of a student getting a college degree in physics may not be to ultimately become a Ph. D. physicist (although that is a path that some physics majors start to pursue after graduation). But, there is a reasonable expectation that our students, once graduated, will be in a technical field of some sort that will require them to present data, calculations, results, whatever-you-want-to-call-it. In a word: numbers. (Oh, numbers with units, of course.) If a student graduates having never worked with significant figures, then writes a technical report for their employer with nonsensical data reporting it could reflect poorly on my department or the college and potentially negatively affect future applicants from our program.

I want my students to be thinking about the proper reporting of their numbers from the start of their physics career. I find that encouraging first-year student to wrestle with the idea of proper data reporting is easier than forcing juniors and seniors to have to go back to the concept of significant figures while they are undertaking more complicated laboratories and undergraduate research projects. If the concept of significant figures is already habit for them, it saves time and effort in the long run.

I believe that many people (you know who you are) either treat significant figures as some fundamental truth, or they haven’t thought about them one way or the other. This is a huge problem when you are sig-fig-stickler.

I'm not (I hope!) a sig-fig stickler. I want my students to be able to follow the general guidelines for using significant figures, but also have the critical thinking skills to be able to break the guidelines, where appropriate.

I've updated a handout that I give to some of my classes (usually general education astronomy classes, although sometime introductory physics classes as well) to emphasize that guidelines are only that: a guide. We should follow them when appropriate, but only when appropriate.